Monday, April 30, 2012

1204.6056 (Mireille Bossy et al.)

Local existence of analytical solutions to an incompressible Lagrangian
stochastic model in a periodic domain
   [PDF]

Mireille Bossy, Joaquin Fontbona, Pierre-Emmanuel Jabin, Jean-François Jabir
We consider an incompressible kinetic Fokker Planck equation in the flat torus. This equation is a simplified version of the Lagrangian stochastic models for turbulent flows introduced by S.B. Pope in the context of computational fluid mechanics. The main difficulties in its treatment arise from the pressure type force in the equation that couples the Fokker Planck equation with a Poisson equation. We prove short time existence of analytic solutions in the one-dimensional case, where we are able to explicit the pressure force and use techniques and functional norms recently introduced in the study of a related singular model.
View original: http://arxiv.org/abs/1204.6056

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